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The closing stock price of Ahmadi, Inc. for a sample of 10 trading days is shown below. What is the 80th percentile? 70.5 55.6 O 66 65.4 61.2 54 60 57 71 54 63 58 62 55 66

The closing stock price of Ahmadi, Inc. for a sample of 10 trading days is shown below. What is the 80th percentile? 70.5 55.6 O 66 65.4 61.2 54 60 57 71 54 63 58 62 55 66

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Calculating the 80th Percentile of Stock Prices The closing stock price of Ahmadi, Inc. over a sample of 10 trading days is recorded as follows: - 54, 57, 54, 58, 55, 60, 71, 63, 62, 66 The question posed is: **What is the 80th percentile?** ### Given Data: - List of closing stock prices (in no particular order) ### Possible Answers: - 70.5 - 55.6 - 66 - 65.4 - 61.2 ### Explanation of Procedure: 1. **Sort the Data:** First, organize the closing prices in ascending order. 2. **Percentile Calculation:** The 80th percentile indicates the value below which 80% of the observations fall. ### Step-by-Step Guide: 1. **Sort the Data:** - Sorted closing stock prices: 54, 54, 55, 57, 58, 60, 62, 63, 66, 71 2. **Determine Position:** - The formula to find the positional rank of the 80th percentile: \( P = \left(\frac{80}{100}\right) \times (N + 1) \) - Where \( N \) is the number of data points. Here, \( N = 10 \). 3. **Calculate the Rank Position:** - \( P = 0.8 \times (10 + 1) = 0.8 \times 11 = 8.8 \) 4. **Find the Corresponding Value:** - The 8.8th position lies between the 8th and 9th values in the sorted list. - To approximate this value, use linear interpolation between the 8th and 9th values. - 8th position value: 63 - 9th position value: 66 5. **Interpolate:** - Interpolated Value = 63 + 0.8(66 - 63) = 63 + 0.8 \times 3 = 63 + 2.4 = 65.4 ### Conclusion: - The 80th percentile of the closing stock prices for Ahmadi, Inc. is **65.4**.
Transcribed Image Text:### Calculating the 80th Percentile of Stock Prices The closing stock price of Ahmadi, Inc. over a sample of 10 trading days is recorded as follows: - 54, 57, 54, 58, 55, 60, 71, 63, 62, 66 The question posed is: **What is the 80th percentile?** ### Given Data: - List of closing stock prices (in no particular order) ### Possible Answers: - 70.5 - 55.6 - 66 - 65.4 - 61.2 ### Explanation of Procedure: 1. **Sort the Data:** First, organize the closing prices in ascending order. 2. **Percentile Calculation:** The 80th percentile indicates the value below which 80% of the observations fall. ### Step-by-Step Guide: 1. **Sort the Data:** - Sorted closing stock prices: 54, 54, 55, 57, 58, 60, 62, 63, 66, 71 2. **Determine Position:** - The formula to find the positional rank of the 80th percentile: \( P = \left(\frac{80}{100}\right) \times (N + 1) \) - Where \( N \) is the number of data points. Here, \( N = 10 \). 3. **Calculate the Rank Position:** - \( P = 0.8 \times (10 + 1) = 0.8 \times 11 = 8.8 \) 4. **Find the Corresponding Value:** - The 8.8th position lies between the 8th and 9th values in the sorted list. - To approximate this value, use linear interpolation between the 8th and 9th values. - 8th position value: 63 - 9th position value: 66 5. **Interpolate:** - Interpolated Value = 63 + 0.8(66 - 63) = 63 + 0.8 \times 3 = 63 + 2.4 = 65.4 ### Conclusion: - The 80th percentile of the closing stock prices for Ahmadi, Inc. is **65.4**.
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